Relative Speed of Boat

Question

On a sunny summer day, you are taking the scenic boat ride from Stein am Rhein, Switzerland, to Schaffhausen, down the Rhein River. This nonstop trip takes 36 minutes, but the return trip to Stein, upstream, will take a full hour. Back in Stein, you decide to stay on the boat and continue on to Constance, Germany, now traveling on the still waters of Lake Constance. How long will this nonstop trip from Stein to Constance take? You may assume that the boat is traveling at a constant speed relative to the water throughout and that the Rhein River flows at a constant speed between Stein and Schaffhausen. The traveling distance from Stein to Schaffhausen is the same as from Stein to Constance.

The boat takes ______ minutes to travel from Stein to Constance.

Answer 1

The current is flowing at 1/4 the boat's speed. Here are the calculations:

(B+C)36 = (B-C)60

36B + 36C = 60B - 60C

96C = 24B

B = 4C

So, B+C = B + (B/4) = 1.25B

Distance/(1.25B) = 36 minutes.

If we multiply by 1.25, we get

D/B=1.25*36 = 45 minutes, and this is the time it would take to go the same distance without any current.

We could also do this:

B-C = B-(B/4) = 0.75B

Distance/(0.75B) = 60 minutes

Multiply both sides by 0.75 and we get

D/B = 0.75*60 = 45 minutes,

and that is a good check on our answer.

We still don't know either the distance, the speed of the boat, nor the speed of the current. But when we can reduce the speeds to multiples of one variable, we can use that to find the time needed to traverse the same distance without the current.